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Results tagged with short-exact-sequences
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user 2191
For questions about short exact sequences in various contexts, including questions on short exact sequences of groups or modules.
4
votes
0
answers
113
views
How can one characterize categories of exact functors?
Does there exist any intrinsic characterization of additive categories equivalent to $\operatorname{Ex}(A,Ab)$, that is, of exact functors from a small abelian category $A$ into abelian groups? Any hi …
- 16.9k
11
votes
Accepted
Does the Grothendieck group depend on the embedding?
I think that the Grothendieck group DOES depend on A. Indeed, any additive category C could be embedded (by the Yoneda embedding) into the abelian category of contravariant additive functors from C to …
- 16.9k
1
vote
0
answers
70
views
On (universal) additive functors making a given complex contractible: examples?
Let $M=(M^i)$ be a (cohomological) complex of objects of some additive category $A$ (I am mostly interested in "short" complexes; yet one may also consider an unbounded $M$). I am interested in those …
- 16.9k